Just expand the search box, like everyone else, and add predefined filters, for example: (see, for example, "view_res_partner_filter")
... <field name="arch" type="xml"> ... <filter string="My First Value" domain="[('my_field','=', 'my_first_value')]"/> <filter string="My Second Value" domain="[('my_field','=', 'my_second_value')]"/> ... </field>
These predefined filters will appear in the "Filters" section under the "search box" and then can be switched by clicking (like your preferred checkbox behavior)
If you insist on using the checkboxes, you will have to do a lot of work, for example, change the corresponding Qweb templates, as well as change the corresponding JS file (see the answer "Burmese Pythis") Therefore, I would prefer this solution if you need time or money.
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